This paper investigates the dynamic response of a coated half-plane subjected to a harmonic Hertz load on the coating surface. The complex modulus is used to describe the hysteretic damping of the elastic homogeneous coating and half-plane. Using the Helmholtz decomposition and Fourier integral transform technique, we derive the stresses and displacements of the coating and half-plane from Navier’s elasticdynamic equations in the form of complex integrals. Then, the global adaptive quadrature algorithm is exploited to solve the complex integrals numerically. The effects of Young’s modulus ratio, density ratio, coating thickness, loss factor and external excitation frequency are discussed. It is found that the dynamic response of displacements and stresses becomes increasingly oscillatory with the increase in excitation frequency.

中文翻译：

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谐波赫兹载荷作用下带迟滞阻尼的半平面动力响应

本文研究了在涂层表面上承受谐波赫兹载荷的涂层半平面的动力响应。复数模量用于描述弹性均质涂层和半平面的滞后阻尼。使用亥姆霍兹分解和傅立叶积分变换技术，我们从Navier的弹性力学方程中以复积分形式导出了涂层和半平面的应力和位移。然后，利用全局自适应正交算法对数值积分进行数值求解。讨论了杨氏模量比，密度比，涂层厚度，损耗因子和外部激励频率的影响。发现随着激励频率的增加，位移和应力的动态响应变得越来越振荡。